A linear circuit containing two sources drives a 100ohm load resistor. Source number 1 delivers 250mW to the load when source number 2 is off. Source number 2 delivers 4W to the load when source number 1 is off. Find the power delivered to the load when both sources are on.
Hint: The answer is not 4.25W. Why

the total output with all independent sources turned on is the algebraic sum of the outputs caused by each source alone

Then if they are in parallel source 2 is giving more voltage, and they will each have a different value of current.
So they will have different power when they have different current.

Is my logic correct, and is there a better way to answer the question?

 

Assume the sources are current sources.

The total combined source power is then proportional to the the sum of the currents squared.

 

If you think in terms of voltage sources you have a problem because one can't allow ideal voltage sources of different value in parallel. They would have to be non-ideal sources with some internal resistance. What you then have is several unknown variables to deal with. Even if you assume one of the sources is ideal and the other non-ideal then the ideal source constrains the power to be either 0.25W or 4W.

Assuming two ideal current sources fits the question constraints without the issues indicated above.

 

What happens when ideal voltage sources are in parallel?

 

They subtract from each other until they equal, acting like resistors?

 

Yes, if the voltage sources are not equal, they will try to equalize each other, creating "short-circuit effects" and producing large currents. Definitely a no-no.